1. Please explain the reasons why (a)the null hypothesis of a hypothesis test
is always assumed a simple one, (b)the hypothesis testing is not used to
support the null hypothesis. 20%
2. In a hypothesis testing, what procedure will you take to decide the
significance value? 10%
3. Consider two groups of data. These two groups of data are sampled
independently. One has a sample size n1 with sample mean x1 and sample
variance s1^2. The other one has a sample size n2 with sample mean x2
and sample variance s2^2. It is to test whether the two groups have the
same mean.
Please show that the following index is proper for t-test. 20%
x1 - x2
t = ----------------------------------
sqrt( (sp^2)/n1) + (sp^2)/n2 )
(n1-1)*s1^2 + (n2-1)*s2^2
with sp^2 = -------------------------------
(n1-1) + (n2-1)
4. Please discuss the possible advantages of spectral analysis in solving
an engineering problem. 20%
5. Please discuss the disadvantages or limitations of spectral analysis. 20%
6. Plaeas discuss the difference between the power spectrum of stochastic
process and the power spectrum of a signal without periodicity. 10%
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